Localized charge distribution , theory

Jensen, J. H. and Gordon, M. S., Ab initio localized charge distributions Theory and a detailed analysis of the water dimer-hydrogen bond, J. Rhys. Chem. 99, 8091-8097 (1995). 

J. H. Jensen and M. S. Gordon, Initio Localized Charge Distributions Theory and Detailed Analysis of the Water Dimer-Hydrogen Bond, J. Phys. Chem. 99, 8091-8107 1995. 

By considering the bare hole as a localized charge distribution which breaks the symmetry of the system, the relaxation process leads to a correlation between the position of the hole and the position of the screening cloud. As a result, the concepts of relaxation and correlation become inseparable. The problem of symmetry breaking, correlation and collective, excitations is well-known in the theory of many-particle sys-tems34-38, and some aspects have recently been considered in applications to excitations of atoms and molecules19,3W2). 

LOCAL CHARGE DISTRIBUTIONS IN METALLIC ALLOYS A LOCAL FIELD COHERENT POTENTIAL APPROXIMATION THEORY... 

EL-HAV = Eisenschitz, London-Hirschfelder, Amos, Van der Avoird FORS = fully optimized reaction space IMPT = intermolecular perturbation theory JS = Jeziorski-Kolos LCD = localized charge distribution MK = Morokuma-Ki-taura MS-MA = Murrell. Shaw-Musher, Amos RS-PT = Rayleigh-Schrodinger perturbation theory RVS = reduced variational space SA = symmetry-adapted perturbation theory SNOPT = symmetric non-orthogonal perturbation theory SRS = symmetrized Rayleigh-Schrddinger. 

A thorough discussion of the basic theory describing electrostatic interactions can be found in [7] the pertinent points are discussed below. Electrostatic forces arise from the osmotic pressure difference between two charged surfaces as a result of the local increase in the ionic distribution around each charged surface. For a single electrified interface, the local ion distribution is coupled to the potential distribution near that surface and can be described using the Poisson-Boltzmann equation. The solution of this equation shows that for low surface potentials the potential follows an exponential function with distance from the interface, D, given by... 

We now outline two approaches to a description of valence in the boron hydrides. The first employs three-center bonds. This particular kind of localized molecular orbital seems most suitable for the smaller, more open hydrides. Its use in the more complex hydrides will require delocalization of the bonding electrons either by a molecular orbital modification or a resonance description. The second approach is simply that of molecular orbitals, which is particularly effective in the more condensed and symmetrical hydrides. These approaches merge as the discussion becomes more complete. It is an important result that filled orbital descriptions are obtainable for the known boron hydrides. Also some remarks about charge distribution in the boron hydrides are possible. But the incompleteness of this valence theory in this nontopological form is indicated by the lack of a large number of unknown hydrides, whose existence would be consistent with these assumptions. 

In earlier studies, whenever a radical-anion was obtained, the ir-charge densities were estimated from ESR parameters 12 13). This is due to the well known assumption that the local spin densities of a radical-ion which can be estimated from the rr charge distribution obtained from ESR can then be compared to the charge distributions obtained from NMR chemical shifts. The exact estimation of empirical parameters of polycyclic ions enables the confrontation of experiment and theory (see Sect. 3.1.3). 

The parabolic form of the Marcus surfaces was obtained from a linear response theory applied to a dielectric continuum model, and we are now in a position to verify this form by using the microscopic definition (16.76) of the reaction coordinate, that is, by verifying that ln(P(A)), where P X) is defined by (16.77), is quadratic in A. Evaluating PIA) is relatively simple in systems where the initial and final charge distributions po and pi are well localized at the donor and acceptor sites so that /)o(r) = - a) + <7b <5(r - rs) and pi (r) = - fa) +... 

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